There are a number of imaging techniques that make it possible to obtain information with two-dimensional (2D) and/or three-dimensional (3D) representations of the interior of a biological organism. This information can be representative of structures and/or biological functions of this organism.
These imaging techniques are non-limitatively grouped together under the name of medical imaging techniques. The biological organism imaged, living or dead, human or non-human, is non-limitatively called the subject.
Certain techniques, such as for example nuclear magnetic resonance imaging (MRI), computed X-ray tomography scanning and positron emission tomography (PET), require sequential acquisitions of data sometimes over long periods of time. The images are then reconstructed by calculation on the basis of these data.
The reconstruction of the images can be significantly degraded by the subject's movements during acquisition, insofar as the structures imaged become deformed over time. This problem is encountered for example during acquisitions of MRI images in the region of the heart or thorax, in particular because of heartbeats and respiratory movements.
It is known to measure these physiological movements during the acquisitions, by means of additional sensors (electrocardiograms, accelerometers, pneumatic belts, etc.) and/or specific acquisition sequences of the imaging system (echo-navigators, partial MRI imaging images) in order to take them into account in the imaging data acquisition and/or processing processes.
According to certain known techniques, the measurements of physiological movements are used to synchronize the acquisitions with these movements. These techniques are however limited to the processing of periodic movements (heartbeats) within fairly restrictive limits.
According to other known techniques, the measurements of perturbations (movements, etc.) are used to generate models of deformations incorporated in the calculation of the images.
In particular, document WO 2009/098371 is known, which describes a method for reconstructing a signal or an image in a medical imaging device on the basis of perturbed measurements.
This method describes the use of a model of the perturbations, such as for example a parametric model describing the elastic physiological movements on the basis of experimental data originating from movement sensors, which is constructed so as to include the perturbations in the problem of reconstruction of the signal. The parametric model describing the perturbations is coupled with a parametric model simulating the signal without perturbation to be reconstructed. These two models are jointly optimized in an iterative process.
A method as described in WO 2009/098371 requires the resolution of linear systems, one of which models the movements, by means of iterative optimization algorithms.
When a linear equation is solved, two problems can be posed:                The large number of unknowns, leading to optimization convergence difficulties;        The use of an explicit regularization, which can distort the convergence of the algorithm.        
The number of unknowns can be particularly high in a parametric model describing the perturbations or movements. It is necessary to evaluate the different components of the displacement due to each independent physiological movement, for each voxel. The number of unknowns in the linear system is therefore for example the following: size of the image×number of degrees of freedom of movement×number of physiological sensors. For example, for an image of size 256×256, with 2 directions of displacement (X and Y) and for 4 physiological movements (thoracic and abdominal respiration and their derivatives), the algorithm must find approximately 500,000 unknowns. If it is now desired to carry out the same processing on 3D data, for a volume of size 256×256×64, with 3 directions of displacement (X, Y and Z) and for 4 physiological movements, the algorithm must find more than 50 million unknowns.
With a linear optimization algorithm, the greater the number of unknowns, the more difficult the convergence of the optimization (long calculation times, convergence towards local minima, numerical instability and inaccuracy of the solution, etc.). The problem so arises for 2D reconstructions with a fine spatial resolution or also with a description of the physiological movement with numerous components. The problem also arises very rapidly for 3D reconstructions.
The problem in general comprises more independent unknowns than independent input data. It can be more or less ill-posed within the meaning of Hadamard's definition. When a problem is ill-posed, it may have several solutions. Some can sometimes even be erroneous.
In order to facilitate the convergence of a linear optimization algorithm, the principle of regularization is often used. This consists of applying an additional constraint to the solution of a problem in order to limit the number of solutions to those that are realistic. For example, a regularization can consist of limiting the displacements solely to those that are relatively smooth or regular (for example by applying constraints to the gradients of a displacement field).
Thus, when an explicit regularization is used, the solution of the linear system is that which both corresponds to the linear equation, and complies with the constraint of explicit regularization.
The constraint used to regularize the optimization of the movement models consists of limiting the displacements solely to those that are relatively smooth or regular (by applying constraints to the gradients of the displacement field). But if this constraint is actually verified within a tissue, this is not necessarily the case at the interface between the organs. These can for example slide against each other. Locally, the movement model then no longer verifies the regularization constraint.
In other words, with the explicit regularization method as found in the prior art, the compromise that must be made between the convergence capacity and the accuracy of the solution is highly detrimental.
An object of the present invention is to propose a method for modelling physiological movements that can be utilized in the context of medical imaging data processing and solves the problems mentioned, in particular concerning the number of unknowns and convergence.
Another object of the present invention is to propose a method for processing medical imaging data, in particular MRI, capable of taking the patient's movements into account.
Another object of the present invention is to propose a method for processing medical imaging data, in particular MRI, which can be implemented in the context of 3D imaging.